Recent efforts on learning cross-domain invariant representations using deep networks generally fall into twocategories.

In this paper, we consider domain-invariant deep learning by explicitly modeling domain shifts with only a small amount of domain-specific parameters in a Convolutional Neural Network (CNN). By exploiting the observation that a convolutional filter can be well approximated as a linear combination of a small set of dictionary atoms, we show for the first time, both empirically and theoretically, that domain shifts can be effectively handled by decomposing a convolutional layer into a domain-specific atom layer and a domain-shared coefficient layer, while both remain convolutional. An input channel will now first convolve spatially only with each respective domain-specific dictionary atom to ``absorb domain variations, and then output channels are linearly combined using common decomposition coefficients trained to promote shared semantics across domains. We use toy examples, rigorous analysis, and real-world examples with diverse datasets and architectures, to show the proposed plug-in framework's effectiveness in cross and joint domain performance and domain adaptation. With the proposed architecture, we need only a small set of dictionary atoms to model each additional domain, which brings a negligible amount of additional parameters, typically a few hundred.

Information Pursuit (IP) is a classical active testing algorithm for predicting an output by sequentially and greedily querying the input in order of information gain. However, IP is computationally intensive since it involves estimating mutual information in high-dimensional spaces. This paper explores Orthogonal Matching Pursuit (OMP) as an alternative to IP for greedily selecting the queries. OMP is a classical signal processing algorithm for sequentially encoding a signal in terms of dictionary atoms chosen in order of correlation gain. In each iteration, OMP selects the atom that is most correlated with the signal residual (the signal minus its reconstruction thus far).

Transformer architectures have achieved remarkable success across language, vision, and multimodal tasks, and there is growing demand for them to address in-context compositional learning tasks. In these tasks, models solve the target problems by inferring compositional rules from context examples, which are composed of basic components structured by underlying rules. However, some of these tasks remain challenging for Transformers, which are not inherently designed to handle compositional tasks and offer limited structural inductive bias. In this work, inspired by the principle of sparse coding, we propose a reformulation of the attention to enhance its capability for compositional tasks. In sparse coding, data are represented as sparse combinations of dictionary atoms with coefficients that capture their compositional rules. Specifically, we reinterpret the attention block as a mapping of inputs into outputs through projections onto two sets of learned dictionary atoms: an encoding dictionary and a decoding dictionary. The encoding dictionary decomposes the input into a set of coefficients, which represent the compositional structure of the input. To enhance structured representations, we impose sparsity on these coefficients. The sparse coefficients are then used to linearly combine the decoding dictionary atoms to generate the output. Furthermore, to assist compositional generalization tasks, we propose estimating the coefficients of the target problem as a linear combination of the coefficients obtained from the context examples. We demonstrate the effectiveness of our approach on the S-RAVEN and RAVEN datasets. For certain compositional generalization tasks, our method maintains performance even when standard Transformers fail, owing to its ability to learn and apply compositional rules.

We propose a multivariate online dictionary-learning method for obtaining decompositions of brain images with structured and sparse components (aka atoms).

We present a semi-unified sparse dictionary learning framework that bridges the gap between classical sparse models and modern deep architectures. Specifically, the method integrates strict Top-$K$ LISTA and its convex FISTA-based variant (LISTAConv) into the discriminative LC-KSVD2 model, enabling co-evolution between the sparse encoder and the dictionary under supervised or unsupervised regimes. This unified design retains the interpretability of traditional sparse coding while benefiting from efficient, differentiable training. We further establish a PALM-style convergence analysis for the convex variant, ensuring theoretical stability under block alternation. Experimentally, our method achieves 95.6\% on CIFAR-10, 86.3\% on CIFAR-100, and 88.5\% on TinyImageNet with faster convergence and lower memory cost ($<$4GB GPU). The results confirm that the proposed LC-KSVD2 + LISTA/LISTAConv pipeline offers an interpretable and computationally efficient alternative for modern deep architectures.

Dictionary learning is traditionally formulated as an $L_1$-regularized signal reconstruction problem. While recent developments have incorporated discriminative, hierarchical, or generative structures, most approaches rely on encouraging representation sparsity over individual samples that overlook how atoms are shared across samples, resulting in redundant and sub-optimal dictionaries. We introduce a parsimony promoting regularizer based on the row-wise $L_\infty$ norm of the coefficient matrix. This additional penalty encourages entire rows of the coefficient matrix to vanish, thereby reducing the number of dictionary atoms activated across the dataset. We derive the formulation from a probabilistic model with Beta-Bernoulli priors, which provides a Bayesian interpretation linking the regularization parameters to prior distributions. We further establish theoretical calculation for optimal hyperparameter selection and connect our formulation to both Minimum Description Length, Bayesian model selection and pathlet learning. Extensive experiments on benchmark datasets demonstrate that our method achieves substantially improved reconstruction quality (with a 20\% reduction in RMSE) and enhanced representation sparsity, utilizing fewer than one-tenth of the available dictionary atoms, while empirically validating our theoretical analysis.